Theory of Complex Scattering Lengths

We derive a generalized Low equation for the T-matrix appropriate for complex atom-molecule interaction. The properties of this new equation at very low energies are studied and the complex scattering length and effective range are derived.Comment: 9 page

The resultant parameters of effective theory

This is the 4-th paper in the series devoted to a systematic study of the problem of mathematically correct formulation of the rules needed to manage an effective field theory. Here we consider the problem of constructing the full set of essential parameters in the case of the most general effective scattering theory containing no massless particles with spin J > 1/2. We perform the detailed classification of combinations of the Hamiltonian coupling constants and select those which appear in the expressions for renormalized S-matrix elements at a given loop order.Comment: 21 pages, 4 LaTeX figures, submitted to Phys. Rev.

Asymptotically Safe Lorentzian Gravity

The gravitational asymptotic safety program strives for a consistent and predictive quantum theory of gravity based on a non-trivial ultraviolet fixed point of the renormalization group (RG) flow. We investigate this scenario by employing a novel functional renormalization group equation which takes the causal structure of space-time into account and connects the RG flows for Euclidean and Lorentzian signature by a Wick-rotation. Within the Einstein-Hilbert approximation, the $\beta$-functions of both signatures exhibit ultraviolet fixed points in agreement with asymptotic safety. Surprisingly, the two fixed points have strikingly similar characteristics, suggesting that Euclidean and Lorentzian quantum gravity belong to the same universality class at high energies.Comment: 4 pages, 2 figure

The UV behavior of Gravity at Large N

A first step in the analysis of the renormalizability of gravity at Large N is carried on. Suitable resummations of planar diagrams give rise to a theory in which there is only a finite number of primitive superficially divergent Feynman diagrams. The mechanism is similar to the the one which makes renormalizable the 3D Gross-Neveu model at large N. Some potential problems in fulfilling the Slavnov-Taylor and the Zinn-Justin equations are also pointed out.Comment: 17 pages, 9 figures. To appear on Phys. Rev. D. Two more references, further technical details and the discussion of the KLT relations at large N have been include

Effective Field Theory for Inflation

The methods of effective field theory are used to study generic theories of inflation with a single inflaton field. For scalar modes, the leading corrections to the ${\cal R}$ correlation function are found to be purely of the $k$-inflation type. For tensor modes the leading corrections to the correlation function arise from terms in the action that are quadratic in the curvature, including a parity-violating term that makes the propagation of these modes depend on their helicity. These methods are also briefly applied to non-generic theories of inflation with an extra shift symmetry, as in so-called ghost inflation.Comment: 14 pages, Latex, references added and minor additions and corrections mad

Note on the thermal history of decoupled massive particles

This note provides an alternative approach to the momentum decay and thermal evolution of decoupled massive particles. Although the ingredients in our results have been addressed in Ref.\cite{Weinberg}, the strategies employed here are simpler, and the results obtained here are more general.Comment: JHEP style, 4 pages, to appear in CQ

The Solar Proton Burning Process Revisited In Chiral Perturbation Theory

The proton burning process p + p -> d + e(+) + \nu(e), important for the stellar evolution of main-sequence stars of mass equal to or less than that of the Sun, is computed in effective field theory using chiral perturbation expansion to the next-to-next-to leading chiral order. This represents a model-independent calculation consistent with low-energy effective theory of QCD comparable in accuracy to the radiative np capture at thermal energy previously calculated by first using very accurate two-nucleon wavefunctions backed up by an effective field theory technique with a finite cut-off. The result obtained thereby is found to support within theoretical uncertainties the previous calculation of the same process by Bahcall and his co-workers.Comment: 30 pages, 2 eps files, aaspp4.sty needed, slightly modified, to be published in Ap.

Higgs-Flavor Groups, Naturalness, and Dark Matter

In the absence of low-energy supersymmetry, a multiplicity of weak-scale Higgs doublets would require additional fine-tunings unless they formed an irreducible multiplet of a non-abelian symmetry. Remnants of such symmetry typically render some Higgs fields stable, giving several dark matter particles of various masses. The non-abelian symmetry also typically gives simple, testable mass relations.Comment: Some comments added after Eqs. (2) and (12

On the Creation of the Universe out of Nothing

We explain how the Universe was created with no expenditure of energy or initial mass.Comment: To be presented at IWARA 2009 (4th International Workshop on Astronomy and Relativistic Astrophysics), to be held in Brazil, October 200

Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional.Comment: Published version, 4 page